{"id":"https://openalex.org/W7214320653","doi":"https://doi.org/10.48550/arxiv.2609.29910","title":"Identities and congruences involving orthogonal polynomials and Ap\u00e9ry-like numbers","display_name":"Identities and congruences involving orthogonal polynomials and Ap\u00e9ry-like numbers","publication_year":2026,"publication_date":"2026-09-24","ids":{"openalex":"https://openalex.org/W7214320653","doi":"https://doi.org/10.48550/arxiv.2609.29910"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.29910","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.29910","pdf_url":"https://arxiv.org/pdf/2609.29910","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.29910","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5152823897","display_name":"Zhi-Hong Sun","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210147117","display_name":"Huaiyin Normal University","ror":"https://ror.org/03xvggv44","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210147117"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Sun, Zhi-Hong","raw_affiliation_strings":["School of Mathematics and Statistics Huaiyin Normal University Huaian , Jiangsu 223300 , P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics Huaiyin Normal University Huaian , Jiangsu 223300 , P.R. China","institution_ids":["https://openalex.org/I4210147117"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5152823897"],"corresponding_institution_ids":["https://openalex.org/I4210147117"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.0044999998062849045,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.00039999998989515007,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"orthogonal polynomials","score":0.9010000228881836},{"id":"https://openalex.org/keywords/congruences","display_name":"congruences","score":0.800000011920929},{"id":"https://openalex.org/keywords/identity","display_name":"identity","score":0.5870000123977661}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7444000244140625},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.6660000085830688},{"id":"https://openalex.org/C9973445","wikidata":"https://www.wikidata.org/wiki/Q8349849","display_name":"Congruence relation","level":2,"score":0.6419000029563904},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.5026999711990356},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4675000011920929},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.43059998750686646},{"id":"https://openalex.org/C52537462","wikidata":"https://www.wikidata.org/wiki/Q5282055","display_name":"Discrete orthogonal polynomials","level":3,"score":0.42179998755455017},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.4104999899864197},{"id":"https://openalex.org/C43176163","wikidata":"https://www.wikidata.org/wiki/Q8023263","display_name":"Wilson polynomials","level":4,"score":0.40799999237060547},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.38679999113082886},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3540000021457672},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3521000146865845},{"id":"https://openalex.org/C201292218","wikidata":"https://www.wikidata.org/wiki/Q740970","display_name":"Recurrence relation","level":2,"score":0.3231000006198883},{"id":"https://openalex.org/C78540521","wikidata":"https://www.wikidata.org/wiki/Q1498246","display_name":"Gegenbauer polynomials","level":4,"score":0.314300000667572},{"id":"https://openalex.org/C135925592","wikidata":"https://www.wikidata.org/wiki/Q2637908","display_name":"Orthogonal functions","level":2,"score":0.3070000112056732},{"id":"https://openalex.org/C86607863","wikidata":"https://www.wikidata.org/wiki/Q5275279","display_name":"Difference polynomials","level":3,"score":0.28610000014305115},{"id":"https://openalex.org/C61349858","wikidata":"https://www.wikidata.org/wiki/Q1568814","display_name":"Hahn polynomials","level":5,"score":0.2791999876499176},{"id":"https://openalex.org/C118797610","wikidata":"https://www.wikidata.org/wiki/Q4298931","display_name":"Kravchuk polynomials","level":5,"score":0.2517000138759613}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.29910","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.29910","pdf_url":"https://arxiv.org/pdf/2609.29910","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.29910","doi":"https://doi.org/10.48550/arxiv.2609.29910","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.29910","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.29910","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.29910","pdf_url":"https://arxiv.org/pdf/2609.29910","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214320653.pdf","grobid_xml":"https://content.openalex.org/works/W7214320653.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W4393336173","https://openalex.org/W4395687127","https://openalex.org/W6922484197","https://openalex.org/W7168402611","https://openalex.org/W7203457180","https://openalex.org/W7214194578"],"related_works":["https://openalex.org/W7203457180","https://openalex.org/W7168402611","https://openalex.org/W2048900920","https://openalex.org/W7097269410","https://openalex.org/W3017079532","https://openalex.org/W7101740808","https://openalex.org/W2093923676","https://openalex.org/W2051305987","https://openalex.org/W1562232356","https://openalex.org/W2085742045"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"establish":[4],"a":[5],"general":[6],"identity":[7],"for":[8],"three-term":[9],"recurrence":[10],"sequences":[11],"and":[12,19],"then":[13],"give":[14],"applications":[15],"to":[16],"orthogonal":[17],"polynomials":[18],"Ap\u00e9ry-like":[20],"numbers.":[21]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-26T00:00:00"}